My PhD thesis (2003)

Some things look differently when viewed through a mirror.

Ben Kilminster in 2003 in Chicago

Searching for Non-Standard Model Couplings in Top Quark Decay

  The Top Quark is the heaviest fundamental particle known to exist in the Standard Model, a theory which explains how particles and forces and fields interact.   Here is a chart showing all the particles in the Standard Model.  Note that in 2003, the Higgs boson was not yet discovered !

Hierarchy of masses

 The light blue color represents uncertainties in the mass.  The neutrinos shown (with greek letter like v) have recently been demonstrated to have mass, although the exact masses have yet to be determined.   Of the particles with masses similar to the top quark, the particle on the far right is the elusive Higgs particle which was not yet detected in 2003, and therefore there were uncertainties on its mass.  

     The fact that the top quark has such a heavy mass, and is comparable to the Higgs mass, hints that the top quark may be special in some way.  Perhaps it behaves differently than the other quarks; perhaps it is intimately related with the Higgs particle, and therefore is part of the mechanism which provides the mass of the other particles ? 

     Of course, all of this is speculation since the Standard Model has proven itself time again as being a theory which holds true with greater than 99.9 % accuracy.   But if there were new physics, one of the best shots to find it is with the heaviest particle, at the highest energies.  In 2003, this meant to analyze data from Fermilab's Tevatron.

How does the analysis work ?

The top quark is heavy, and does not exist stably in nature.  With a high-energy accelerator, one can use the energy from the collision of particles to create the mass of the top quark.  This can be understood with Einstein's famous formula (E=mc^2), which means that Energy (E) and mass (m) are different forms of the same thing and can be interchanged.   

Now that we have a top quark, because it is unstable, it "decays".  This means that a force transforms the top quark into two slightly more stable particles, a W boson and a b quark.   In this case, the force is the weak force, which is the same force that causes the sun to burn by transforming hydrogen into helium. The top quark decays so fast that if 1 trillion (1,000,000,000,000) top quarks all decayed one after another, the whole thing would be over in one trillionth of a second (0.000000000001 s).   This isn't the end of the story, since the W boson will decay into more stable particles, like an electron and neutrino, and the b quark will turn into a spray of particles called a b "jet", which in turn decay into more stable particles, until they are the same as the matter we are made of.  We can measure the electron and the b jet in our detector. 

The weak force that allows the top quark to decay into the lighter particles, the W and b quark (see Chart of masses above ), is weird in that it has been measured to be left-handed. 

It is this asymmetry which my analysis is testing.  If the asymmetry were exactly the opposite of what the Standard Model says, as is the case in some models where the top quark is "special", then one could study the angle between the electron and b-jet in top quark decay data, and determine that the asymmetry is different than was expected. 

In other words, one makes a model of two different theories, and then compares them with the data.  In the next plot, there are two theories, the blue line is what the Standard Model says the answer should be, and the red line is an alternate theory.  

Two theories for top-quark decay : 

Two theories showing possible ways the top quark decays

If the data looks more like the red line, and the errors are small enough, then one can say that the Standard Model is not correct with a certain amount of confidence. 

That is how my analysis works basically.   However, there are some complications : 

1)  Top quark decays are rare.  One must find 100 top quark decays in 1,000,000,000,000 collisons.   

2)  There are lots of other physics processes and particle decays that look like top quark decay. We have to figure out what can mimic a top quark decay, and how often.

3)  We have to make mathematical models of what top quark decays would look like,  and run computer simulations which would reproduce the conditions of our detector to show us what the detector sees when top quarks decay.

4)  We have to identify all the possible sources of uncertainty that could cause us to get different answers.   Then we have to simulate the effect of these uncertainties on our measurement. 

5)  Finally, we have to look at the data and make a measurement, which tells us which mathematical model of the top quark decay is correct.   We calculate a number with uncertainties coming from (4) and coming from finite statistics of our dataset.  (For instance, if we made a measurement from 1000 top-quark decays,  we would be more confident in our answer than if we only had 1 top quark decay.)

6)  So now we have a number with uncertainties.  We then seek approval from our collaborators who scrutinize our analysis technique until they feel that it is correct, and there are no mistakes.  Often times, we will have to redo some part of the analysis in order to satisfy our fellow experimenters.

7)   Now we can make our results public and present them at conferences and publish them in journals, where these results, and the results of many other physicists, will be combined together to understand the big picture.

My final result is that the top quark decays according to the blue line above, rather than the red line, with more than a 95% probability. Therefore, it looks like the Standard Model has remained unscathed once again !!